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25 Nov 2018

Leaving Certificate Examination 1965 Honours Applied Mathematics

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Question 1

Two pegs are fixed at points quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds and quicklatex.com-e24826b0fac28861acd034428af346f0_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds in the same horizontal line. One end of a light string is attached to quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds and the other end to quicklatex.com-e24826b0fac28861acd034428af346f0_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds. When masses of quicklatex.com-dc2e717421b16a9f080dba4c8c0e3437_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds and quicklatex.com-3883c8dfa7e1fd380cd2fa2674d982e2_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds lb. are attached to points quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds and quicklatex.com-e86ae6aeacc8696c140ee1ca29d51f96_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds, respectively, on the string, the quicklatex.com-5e10c31486800c33ecc695d7ebf3cfab_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds and quicklatex.com-d7aef44dfb015d695f0f48732466d47b_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds. Find the tension, in lb. wt., in each of the segments quicklatex.com-bb11fdb4c82e898ea8147471416d775f_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds, quicklatex.com-3675ba693016b80ac93fbf734e15678b_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds, quicklatex.com-090252563a7d95933f4046a6c256de5b_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds of the string, correct in each case to one significant figure.

Question 2

Three particles weighing quicklatex.com-d189c7271c0685c98d20113a661f3d4e_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds, quicklatex.com-16597321624aaf57e2abd3410e1aa0b4_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds, quicklatex.com-58512c521f3f30db10c129b09bc0a282_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds are placed, respectively, at points the coordinates of which are quicklatex.com-b5217e2e6f42150690fb981d4a22953f_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds, quicklatex.com-5a2eab4aa4ff9c017536572b74bce79b_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds, quicklatex.com-7ec3d0be6b72960b1ec4424a68f94810_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds. If quicklatex.com-35432dfe2e6ae9b47e0bf79e65a5549d_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds are the coordinates of the centre of gravity of the system, show that

quicklatex.com-e61d8b92645eeb2fd5a78c7f44cda633_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds, quicklatex.com-2bc3e1a40d865a5e6c33c347c605ef18_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds

Particles of weight quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds, quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds, quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds and quicklatex.com-fd6542ae3d49d38a0f73fefe83b285af_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds grams are placed, respectively, at the points quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds, quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds, quicklatex.com-e86ae6aeacc8696c140ee1ca29d51f96_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds, quicklatex.com-e24826b0fac28861acd034428af346f0_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds, the coordinate of which are quicklatex.com-32f7d76a99d59af414e8fc78e1089ad9_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds, quicklatex.com-27dd1fabb46aa13303533c87afebe623_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds, quicklatex.com-5cb6787c0e19022bda5029e9be24290b_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds, quicklatex.com-96793687f6d8103ad39cc3d29782138e_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds respectively. Find the position of the centre of gravity of the system.

What additional weight must be placed at quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds if the centre of gravity is required to be at the mid-point of quicklatex.com-371fe833e9a89e2790fc66adb618b944_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds?

Question 3

What is meant by the velocity of a particle relative to another particle?

Explain, with the aid of a diagram, how the velocity of quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds relative to quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds may be found if the velocities of quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds and quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds are known.

The velocity of a ship relative to a steady wind is quicklatex.com-2dda138cd42bede9cb97214fc5c8a205_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds m.p.h. in the direction quicklatex.com-db038f317452921bf729a1d1efed0d24_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds North of East and the velocity of a boat relative to the same wind is quicklatex.com-739f6781b65065fc445d5f13b544d6b2_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds m.p.h. in the direction quicklatex.com-209c1958604e9f7d31e020b608033e83_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds South of West. Find the velocity (in magnitude and direction) of the ship relative to the  boat.

Question 4

A car weighing quicklatex.com-8a0f60b8ca3ec09a3984d53508863c9a_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds cwt. is descending an incline of quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds in quicklatex.com-1c2411091e17c31612a16015839f2c94_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds. The speed of the car is quicklatex.com-9e7ec55fdcc4467668102a4d17def052_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds m.p.h. and it is accelerating at the rate of quicklatex.com-cbffa69e3668a30e97f5514c17043a64_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds ft. per sec.quicklatex.com-025303222356a63c2332a429c33d35a9_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds. If the frictional resistance to motion is equivalent to quicklatex.com-2dda138cd42bede9cb97214fc5c8a205_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds lb. wt., find the horse-power at which the car is working.

If the car travels in a straight line on a horizontal track against a frictional resistance to motion of quicklatex.com-7260fe4f20eb47e11e44b79da133e21c_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds lb. wt., find the greatest speed it attains if it develops quicklatex.com-3883c8dfa7e1fd380cd2fa2674d982e2_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds horse-power.

Question 5

If three forces acting at a point are in equilibrium, prove that each force is proportional to the sine of the angles between the lines of action of the other two forces. The perpendiculars drawn from the vertices of an acute – angled triangle meet at quicklatex.com-5b090119e833ac90162777d07e3fe243_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds. The perpendiculars from quicklatex.com-5b090119e833ac90162777d07e3fe243_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds to the sides of the triangles are the lines of action of three forces. Each force acts away from quicklatex.com-5b090119e833ac90162777d07e3fe243_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds and is proportional to the length of the side to which it is perpendicular. Prove that the three forces are in equilibrium.

Question 6

Derive an expression, in terms of the angle of projection and the initial velocity, for (i) the range, (ii) the greatest height reached by a projectile.

Two particles are projected from a point quicklatex.com-5b090119e833ac90162777d07e3fe243_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds with the same initial velocity at angles of elevation quicklatex.com-ff89c3adde787f392f47810bb5512a17_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds and quicklatex.com-b9306d10a390d056ce56692d212481c3_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds. If quicklatex.com-afd7350d38206954a50223929229ee4c_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds, show that the range of each of the two particles is the same.

If the initial velocity of each of the particles if quicklatex.com-a596ad4d5102039f1aaadb9079aa1b05_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds ft. per second and quicklatex.com-7bc4f1f0f4c11887bbe547ac256853e5_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds ft. is the greatest height reached by one of the particles, find the greatest height reached by the other particle.

Question 7

Define simple harmonic motion.

A particle is moving in a striaght line with simple harmonic motion. When it is quicklatex.com-dc2e717421b16a9f080dba4c8c0e3437_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds cm. from its mean position, its velocity and acceleration are quicklatex.com-dc2e717421b16a9f080dba4c8c0e3437_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds cm. per sec. and quicklatex.com-dc2e717421b16a9f080dba4c8c0e3437_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds cm. per sec.quicklatex.com-025303222356a63c2332a429c33d35a9_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds, respectively. Find

(i) the greatest velocity of the particle,

(ii) the period of the motion,

(iii) the average velocity of the particle as it travels from rest to rest.

Question 8

A circular piece of tin rotates at the rate of quicklatex.com-9e7ec55fdcc4467668102a4d17def052_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds revolutions per minute about an axis through its centre quicklatex.com-5b090119e833ac90162777d07e3fe243_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds, the axis being perpendicular to the plane of the tin. quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds and quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds are two poitns on the tin such that quicklatex.com-585661d283e3f2fa1785620a0a40eb21_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds inches, quicklatex.com-f6566d03614491b73380e329095751fd_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds ft. quicklatex.com-ee873c946a42a316d07b2d164e2b7d67_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds ins. and quicklatex.com-fb411c1981073732361d225e48642413_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds. Weights of quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds lb. and quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds lb. are placed, respectively, at quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds and quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds. Find the magnitude and direction of the resultant centrifugal force on the axis.

If quicklatex.com-e86ae6aeacc8696c140ee1ca29d51f96_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds is a point on the tin such that quicklatex.com-34b58ba01d079e46981dee26d0c9105b_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds ft., quicklatex.com-a9e7434869701a9a91df91e1648b3349_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds and quicklatex.com-1e3376a84708823c79979dc6ad940442_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds, what weight must be placed at quicklatex.com-e86ae6aeacc8696c140ee1ca29d51f96_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds if the resultant centrifugal force is to act along quicklatex.com-10d7b3f9c2cfee3c3af0d6b6e9a1886f_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds?

Question 9

A vessel in the shape of a cube has internal edges each quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds ft. long. A liquid fills the vessel to a height of quicklatex.com-ee873c946a42a316d07b2d164e2b7d67_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds inches and a second liquid which does not mix the the first occupies the remainder of the vessel. On each vertical side the total thrust on that part in contact with one liquid is equal to the total thrust on that part in contact with the other. Show that the specific gravities of the two liquids are in the ratio quicklatex.com-54bac54b928d1707dc50fa2ecb36d74d_l3 | Leaving Certificate Examination 1965 Honours Applied Mathematics | Maths Grinds.


Citation:

State Examinations Commission (2018). State Examination Commission. Accessed at: https://www.examinations.ie/?l=en&mc=au&sc=ru

Malone, D and Murray, H. (2016). Archive of Maths State Exams Papers. Accessed at: http://archive.maths.nuim.ie/staff/dmalone/StateExamPapers/

Licence:

“Contains Irish Public Sector Information licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) licence”.

The EU Directive 2003/98/EC on the re-use of public sector information, its amendment EU Directive 2013/37/EC, its transposed Irish Statutory Instruments S.I. No. 279/2005, S.I No. 103/2008, and S.I. No. 525/2015, and related Circulars issued by the Department of Finance (Circular 32/05), and Department of Public Expenditure and Reform (Circular 16/15 and Circular 12/16).

Note. Circular 12/2016: Licence for Re-Use of Public Sector Information adopts CC-BY as the standard PSI licence, and notes that the open standard licence identified in this Circular supersedes PSI General Licence No: 2005/08/01.

Links:

https://circulars.gov.ie/pdf/circular/per/2016/12.pdf

https://creativecommons.org/licenses/by/4.0/legalcod

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